Number of cysts on 11 potato genotypes for 5 potato cyst nematode populations.

The number of cysts on 11 potato genotypes for 5 potato cyst nematode populations.

data("vaneeuwijk.nematodes")

Format

A data frame with 55 observations on the following 3 variables.

gen

potato genotype

pop

nematode population

y

number of cysts

Details

The number of cysts on 11 potato genotypes for 5 potato cyst nematode populations belonging to the species Globodera pallida. This is part of a larger table in . The numbers are the means over four or five replicates.

Van Eeuwijk used this data to illustrate fitting a generalized linear model.

Source

Fred A. van Eeuwijk, (1995). Multiplicative Interaction in Generalized Linear Models. Biometrics, 51, 1017-1032. https://doi.org/10.2307/2533001

References

Arntzen, F.K. & van Eeuwijk (1992). Variation in resistance level of potato genotypes and virulence level of potato cyst nematode populations. Euphytica, 62, 135-143. https://doi.org/10.1007/BF00037939

Examples

library(agridat)
data(vaneeuwijk.nematodes)
dat <- vaneeuwijk.nematodes

# show non-normality
op <- par(mfrow=c(2,1), mar=c(5,4,3,2))
boxplot(y ~ pop, data=dat, las=2,
        ylab="number of cysts")
title("vaneeuwijk.nematodes - cysts per nematode pop")
boxplot(y ~ gen, data=dat, las=2)
title("vaneeuwijk.nematodes - cysts per potato")
par(op)

# \dontrun{
  # normal distribution
  lm1 <- lm(y ~ gen + pop, data=dat)

  # poisson distribution
  glm1 <- glm(y ~ gen+pop,data=dat,family=quasipoisson(link=log))
  anova(glm1)
#> Analysis of Deviance Table
#> 
#> Model: quasipoisson, link: log
#> 
#> Response: y
#> 
#> Terms added sequentially (first to last)
#> 
#> 
#>      Df Deviance Resid. Df Resid. Dev
#> NULL                    54     8947.4
#> gen  10   7111.4        44     1836.0
#> pop   4    690.6        40     1145.4

  libs(gnm)

  # main-effects non-interaction model
  gnm0 <- gnm(y ~ pop + gen, data=dat,
              family=quasipoisson(link=log))
  # one interaction
  gnm1 <- gnm(y ~ pop + gen + Mult(pop,gen,inst=1), data=dat,
              family=quasipoisson(link=log))
#> Initialising
#> Running start-up iterations..
#> Running main iterations.........................................................
#> ..........................
#> Done
  # two interactions
  gnm2 <- gnm(y ~ pop + gen + Mult(pop,gen,inst=1) + Mult(pop,gen,inst=2),
              data=dat,
              family=quasipoisson(link=log))
#> Initialising
#> Running start-up iterations..
#> Running main iterations.............
#> Done

  # anova(gnm0, gnm1, gnm2, test="F")
  # only 2, not 3 axes needed

  # match vaneeuwijk table 2
  # anova(gnm2)
  ##                          Df Deviance Resid. Df Resid. Dev
  ## NULL                                        54     8947.4
  ## pop                       4    690.6        50     8256.8
  ## gen                      10   7111.4        40     1145.4
  ## Mult(pop, gen, inst = 1) 13    716.0        27      429.4
  ## Mult(pop, gen, inst = 2) 11    351.1        16       78.3

  # compare residual qq plots from models
  op <- par(mfrow=c(2,2))
  plot(lm1, which=2, main="LM")
  plot(glm1, which=2, main="GLM")
  plot(gnm0, which=2, main="GNM, no interaction")
  plot(gnm2, which=2, main="GNM, 2 interactions")
  par(op)

  # extract interaction-term coefficients, make a biplot
  pops <- pickCoef(gnm2, "[.]pop")
  gens <- pickCoef(gnm2, "[.]gen")
  coefs <- coef(gnm2)
  A <- matrix(coefs[pops], nc = 2)
  B <- matrix(coefs[gens], nc = 2)
  A2=scale(A)
  B2=scale(B)
  rownames(A2) <- levels(dat$pop)
  rownames(B2) <- levels(dat$gen)
  # near-match with vaneeuwijk figure 1
  biplot(A2,B2, expand=2.5,xlim=c(-2,2),ylim=c(-2,2),
         main="vaneeuwijk.nematodes - GAMMI biplot")

# }